Stability Analysis of Lur´e-Type Switched Systems

This technical note aims to introduce stability analysis of Lur´e-type switched systems in frequency domain. A new state-input dependent switching function is proposed and it is the key issue to obtain a stability condition that generalizes the celebrated Popov criterion to deal with this class of switched nonlinear systems. Likewise the case of time invariant systems, we propose a frequency domain stability test that is expressed through a convex combination of the subsystems state space matrices. This task is not trivial due to the time-varying nature of the nonlinear systems under consideration. The theory is illustrated by a simple example.